Statistics and Computing

, Volume 5, Issue 3, pp 245–252

A simple, automatic and adaptive bivariate density estimator based on conditional densities

  • Jeffrey S. Simonoff

DOI: 10.1007/BF00142666

Cite this article as:
Simonoff, J.S. Stat Comput (1995) 5: 245. doi:10.1007/BF00142666


The standard approach to non-parametric bivariate density estimation is to use a kernel density estimator. Practical performance of this estimator is hindered by the fact that the estimator is not adaptive (in the sense that the level of smoothing is not sensitive to local properties of the density). In this paper a simple, automatic and adaptive bivariate density estimator is proposed based on the estimation of marginal and conditional densities. Asymptotic properties of the estimator are examined, and guidance to practical application of the method is given. Application to two examples illustrates the usefulness of the estimator as an exploratory tool, particularly in situations where the local behaviour of the density varies widely. The proposed estimator is also appropriate for use as a ‘pilot’ estimate for an adaptive kernel estimate, since it is relatively inexpensive to calculate.


Kernel density estimation smoothing parameter selection 

Copyright information

© Chapman & Hall 1995

Authors and Affiliations

  • Jeffrey S. Simonoff
    • 1
  1. 1.Department of Statistics and Operations ResearchNew York UniversityNew YorkUSA

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